ON THE LIMIT CYCLES OF A CLASS OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS

被引：2
|
作者：
Llibre, Jaume [1 ]
Menezes, Lucyjane de A. S. [2 ]
机构：
[1] Univ Autonoma Barcelona, Dept Matemat, E-08193 Barcelona, Catalonia, Spain
[2] Univ Fed Goias, Inst Matemat & Estat, BR-74690900 Goiania, Go, Brazil
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B | 2020年 / 25卷 / 05期
基金：
欧盟地平线“2020”;
关键词：
Discontinuous systems; Poincare map; return map; limit cycles;
D O I：
10.3934/dcdsb.2020005
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider discontinuous piecewise linear differential systems whose discontinuity set is a straight line L which does not pass through the origin. These systems are formed by two linear differential systems of the form (x) over dot = Ax +/- b. We study the limit cycles of this class of discontinuous piecewise linear differential systems. We do this study by analyzing the fixed points of the return map of the system defined on the straight line L. This kind of differential systems appear in control theory.
引用
收藏
页码：1835 / 1858
页数：24
相关论文
共 50 条
  • [1] The limit cycles of a class of discontinuous piecewise differential systems
    Baymout, Louiza
    Benterki, Rebiha
    Llibre, Jaume
    INTERNATIONAL JOURNAL OF DYNAMICAL SYSTEMS AND DIFFERENTIAL EQUATIONS, 2024, 13 (04)
  • [2] LIMIT CYCLES OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS
    Cardin, Pedro Toniol
    De Carvalho, Tiago
    Llibre, Jaume
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2011, 21 (11): : 3181 - 3194
  • [3] Limit Cycles and Bifurcations in a Class of Discontinuous Piecewise Linear Systems
    Li, Tao
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2019, 29 (10):
  • [4] TWO LIMIT CYCLES FOR A CLASS OF DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH TWO PIECES
    Berbache, A.
    SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA, 2020, 17 : 1488 - 1515
  • [5] Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems
    Mereu, Ana C.
    Oliveira, Regilene
    Rodrigues, Camila A. B.
    NONLINEAR DYNAMICS, 2018, 93 (04) : 2201 - 2212
  • [6] On the limit cycles for a class of discontinuous piecewise cubic polynomial differential systems
    Huang, Bo
    ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2020, (25) : 1 - 24
  • [7] Limit cycles for a class of discontinuous piecewise generalized Kukles differential systems
    Ana C. Mereu
    Regilene Oliveira
    Camila A. B. Rodrigues
    Nonlinear Dynamics, 2018, 93 : 2201 - 2212
  • [8] Limit Cycles in a Class of Continuous-Discontinuous Piecewise Linear Differential Systems with Three Zones
    Berbache, Aziza
    INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2024, 34 (15):
  • [9] On limit cycles bifurcating from the infinity in discontinuous piecewise linear differential systems
    Gouveia, Marcio R. A.
    Llibre, Jaume
    Novaes, Douglas D.
    APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 : 365 - 374
  • [10] ON THE LIMIT CYCLES OF PLANAR DISCONTINUOUS PIECEWISE LINEAR DIFFERENTIAL SYSTEMS WITH A UNIQUE EQUILIBRIUM
    Li, Shimin
    Llibre, Jaume
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, 2019, 24 (11): : 5885 - 5901
12345